Experimental Investigation of Quantum $\mathcal{P}\mathcal{T}$-Enhanced Sensor

$\mathcal{P}\mathcal{T}$-symmetric theory is developed to extend quantum mechanics to a complex region, but it wins its great success first in classical systems, for example, optical waveguides and electric circuits, etc., because there are so many counterintuitive phenomena and striking applications, including unidirectional light transport, $\mathcal{P}\mathcal{T}$-enhanced sensors (one kind of exceptional-point-based sensor), and wireless power transfer. However, these phenomena and applications are mostly based on the ability to approach a $\mathcal{P}\mathcal{T}$-symmetric broken region, which makes it difficult to transfer them to the quantum regime, since the broken quantum $\mathcal{P}\mathcal{T}$-symmetric system has not been constructed effectively, until recently several methods have been raised. Here, we construct a quantum $\mathcal{P}\mathcal{T}$-symmetric system assisted by weak measurement, which can effectively transit from the unbroken region to the broken region. The full energy spectrum including the real and imaginary parts is directly measured using weak values. Furthermore, based on the ability of approaching a broken region, we for the first time translate the previously mentioned $\mathcal{P}\mathcal{T}$-enhanced sensor into the quantum version, and investigate its various features that are associated to the optimal conditions for sensitivity enhancement. In this experiment, we obtain an enhancement of 8.856 times over the conventional Hermitian sensor. Moreover, by separately detecting the real and imaginary parts of energy splitting, we can derive the additional information of the direction of perturbations. Our work paves the way of leading classical interesting $\mathcal{P}\mathcal{T}$ phenomena and applications to their quantum counterparts. More generally, since the $\mathcal{P}\mathcal{T}$ system is a subset of non-Hermitian systems, our work will be also helpful in the studies of general exception point in the quantum regime.

Figure 1

(a) Logic diagram of the construction of $\mathcal{P}\mathcal{T}$-symmetric system. (b) Experimental setup. Both the diagram and setup are divided into 6 modules: (1) The system preparation and dilation; (2) preselection state preparation; (3) pointer state preparation; (4) coupling of the pointer and dilated system in which the $\mathcal{P}\mathcal{T}$-symmetric system is embedded; (5) postselection; (6) weak value readout. Half-wave plate (HWP); quarter-wave plate (QWP); beam splitter (BS); polarizing beam splitter (PBS); phase plate (PP); beam displacer (BD); periodically poled potassium titanyl phosphate (ppKTP); band-pass filter (BF); single-photon avalanche diode (SPAD).

Figure 2

Energy spectrum $E_{+}(s)$ of the $\mathcal{P}\mathcal{T}$-symmetric system directly measured by weak value $⟨\tilde{H}(s){⟩}_{\mathrm{w}}^{+}$. The black circles with error bars are real and imaginary parts of the weak value, and the red lines are the corresponding eigenenergy directly calculated from the $\mathcal{P}\mathcal{T}$-symmetric Hamiltonian Eq. (1); i.e., $E_{+}(s){|}_{r=\sqrt{2},\theta =\pi /4}=1+\sqrt{s^2-1}$.

Figure 3

Response of normalized energy splitting $\mathrm{\Delta }E$ to amplitude of perturbation $\epsilon$. $r=\sqrt{2}$ and $\theta =\pi /2$. Similarly, only one part does not vanish, and black circles and red lines represent the experimental results and theoretical values, respectively.